LONDON — Last year, Prime Minister David Cameron of Britain used his appearance at the World Economic Forum to vent frustration with the European Union, listing some of the policies he would ditch if he could throw off Europe’s regulatory shackles.

“In the name of social protection, the EU has promoted unnecessary measures that impose burdens on businesses and governments, and can destroy jobs,” he argued, adding a list of directives that he would like to scrap.

One year later, Cameron is following through on that pledge. He is promising to renegotiate Britain’s ties to the 27-nation bloc, forge a new and looser relationship, and is expected to say on Wednesday that he would put the outcome of those talks to a referendum.

A speech on Europe, planned for last week, was postponed because of the crisis in Algeria. It has been rescheduled for Wednesday, ahead of a possible visit by Cameron to Davos, Switzerland.

It was unclear whether Cameron would attend Davos this year and speak on the same theme. But his tough line on Europe echoes growing British disenchantment with a bloc whose single currency union, which the British never joined, has been in crisis for three years.

Yet, supposing Cameron were to succeed in scaling down Britain’s involvement, some central questions will arise. Can Britain play a more limited role in Brussels and still retain significant influence there? And what might that mean for Britain’s full participation in one of the world’s biggest single markets?

In their 40-year history of engagement with a unifying Europe, Britons have never embraced the idea of unity; instead they have seen their ties to the Continent in pragmatic terms. Increasingly, London’s conclusion seems to be that the costs in terms of regulatory burdens and financial contributions are not outweighed by clear benefits.

Cameron argues that to stabilize support for the European Union in Britain, the relationship must be loosened and focused more on the bloc’s single market of almost 500 million people.

Britain, which is in the second tier of EU membership, not only stayed out of the euro — and unlike most of the others on the sidelines has no intention of joining — but also does not participate in Europe’s Schengen passport-free travel zone. The British government also announced last year that it would opt out of a range of justice and security policy areas.

A group of Conservative lawmakers argued last week for five treaty changes, including those that would allow any country to block new EU legislation on financial services, and would repatriate social and employment laws to national capitals. Britain’s euro skeptics are also blunt in their criticism of the bloc’s agricultural, fisheries and regional aid programs

Many would ideally like to keep just one element of EU membership: access to the single market. Although achieving such status looks highly improbable.